This Letter proposes a solution of the Vacuum Energy and the Cosmological Constant (CC)paradox based on the Zel'dovich's ansatz, which states that the observable contribution to thevacuum energy density is given by the gravitational energy of virtual particle-antiparticle pairs,continually generated and annihilated in the vacuum state. The novelty of this work is the use of anultraviolet cut-off length based on the Holographic Principle, which is shown to yield current valuesof the CC in good agreement with experimental observations.

We compute to high post-Newtonian accuracy the 4-momentum (linear momentum and energy), radiatedas gravitational waves in a two-body system undergoing gravitational scattering. We include, for the firsttime, all the relevant time-asymmetric effects that arise when consistently going three post-Newtonianorders beyond the leading post-Newtonian order. We find that the inclusion of time-asymmetric radiativeeffects (both in tails and in the radiation-reacted hyperbolic motion) is crucial to ensure the masspolynomiality of the post-Minkowskian expansion (G expansion) of the radiated 4-momentum. Imposingthe mass polynomiality of the corresponding individual impulses determines the conservativelikeradiative contributions at the fourth post-Minkowskian order and strongly constrains them at the fifthpost-Minkowskian order.

We compute the leading order contribution to radiative losses in the case of spinning binaries with alignedspins due to their spin-orbit interaction. The orbital average along hyperboliclike orbits is taken through anappropriate spin-orbit modification to the quasi-Keplerian parametrization for nonspinning bodies, whichmaintains the same functional form, but with spin-dependent orbital elements. We perform consistencychecks with existing post-Newtonian-based and post-Minkowskian (PM)-based results. In the former case,we compare our expressions for both radiated energy and angular momentum with those obtained in [G. Choet al., From boundary data to bound states. Part III. Radiative effects,J. High Energy Phys. 04 (2022) 154] byapplying the boundary-to-bound correspondence to known results for ellipticlike orbits, finding agreement.The linear momentum loss is instead newly computed here. In the latter case, we also find agreement with thelow-velocity limit of recent calculations of the total radiated energy, angular momentum and linearmomentum in the framework of an extension of the worldline quantum field theory approach to the classicalscattering of spinning bodies at the leading PM order [G. U. Jakobsen et al., Gravitational Bremsstrahlungand Hidden Supersymmetry of Spinning Bodies, Phys. Rev. Lett. 128, 011101 (2022), M. M. Riva et al.,Gravitational bremsstrahlung from spinning binaries in the post-Minkowskian expansion, Phys. Rev. D 106,044013 (2022)]. We get exact expressions of the radiative losses in terms of the orbital elements, even if theyare at the leading post-Newtonian order, so that their expansion for large values of the eccentricity parameter(or equivalently of the impact parameter) provides higher-order terms in the corresponding PM expansion,which can be useful for future crosschecks of other approaches.

We compare recent one-loop-level, scattering-amplitude-based, computations of the classical partof the gravitational bremsstrahlung waveform to the frequency-domain version of the corresponding Multipolar-Post-Minkowskianwaveform result. When referring the one-loop result to the classical averaged momenta $\bar p_a = \frac12 (p_a+p'_a)$,the two waveforms are found to agree at the Newtonian and first post-Newtonian levels,as well as at the first-and-a-half post-Newtonian level, i.e. for the leading-order quadrupolar tail.However, we find that there are significant differences at the second-and-a-half post-Newtonian level,$O\left( \frac{G^2}{c^5} \right)$, i.e.when reaching: (i) the first post-Newtonian correction to the linear quadrupole tail; (ii) Newtonian-level linear tailsof higher multipolarity (odd octupole and even hexadecapole); (iii) radiation-reaction effects on the worldlines;and (iv) various contributions of cubically nonlinear origin (notably linked tothe quadrupole$\times$ quadrupole$\times$ quadrupole coupling in the wavezone).These differences are reflected at the sub-sub-sub-leading level in the soft expansion, $ \sim \om \ln \om $, i.e. $O\left(\frac{1}{t^2} \right)$in the time domain.Finally, we computed the first four terms of the low-frequency expansion of the Multipolar-Post-Minkowskian waveform and checkedthat they agree with the corresponding existing classical soft graviton results.

Based on a previous ansatz by Zel'dovich for the gravitational energy of virtualparticle-antiparticle pairs, supplemented with the Holographic Principle, we estimate the vacuumenergy in a fairly reasonable agreement with the experimental values of the Cosmological Constant.We further highlight a connection between Wheeler's quantum foam and graviton condensation,as contemplated in the quantum N-portrait paradigm, and show that such connection also leads toa satisfactory prediction of the value of the cosmological constant. The above results suggest thatthe "unnaturally" small value of the cosmological constant may find a quite "natural" explanationonce the nonlocal perspective of the large N-portrait gravitational condensation is endorsed.

The class of Petrov type I curvature tensors is further divided into those for whichthe span of the set of distinct principal null directions has dimension four (maximallyspanning type I) or dimension three (nonmaximally spanning type I). Explicit examplesare provided for both vacuum and nonvacuum spacetimes.

Taking wedge products of the p distinct principal null directions (PNDs) associated with the eigen-bivectors of the Weyl tensor associated with the Petrov classification, when linearly independent, one is able to express them in terms of the eigenvalues governing this decomposition. We study here algebraic and differential properties of such p-forms by completing previous geometrical results concerning type I spacetimes and extending that analysis to algebraically special spacetimes with at least two distinct PNDs. A number of vacuum and nonvacuum spacetimes are examined to illustrate the general treatment.

Mass currents in astrophysics generate gravitomagnetic fields of enormous complexity. Gravitomagnetichelicity, in direct analogy with magnetic helicity, is a measure of entwining of the gravitomagnetic fieldlines. We discuss gravitomagnetic helicity within the gravitoelectromagnetic (GEM) framework oflinearized general relativity. Furthermore, we employ the spacetime curvature approach to GEM in orderto determine the gravitomagnetic helicity for static observers in Kerr spacetime.

In the description of the relativistic two-body interaction, together with the effects of energy andangular momentum losses due to the emission of gravitational radiation, one has to take into account alsothe loss of linear momentum, which is responsible for the recoil of the center-of-mass of the system. Wecompute higher-order tail (i.e., tail-of-tail and tail-squared) contributions to the linear momentum fluxfor a nonspinning binary system either along hyperboliclike or ellipticlike orbits. The correspondingorbital averages are evaluated at their leading post-Newtonian approximation, using harmoniccoordinates and working in the Fourier domain. The final expressions are given in a large-eccentricity(or large-angular momentum) expansion along hyperboliclike orbits and in a small-eccentricityexpansion along ellipticlike orbits. We thus complete a previous analysis focusing on both energyand angular momentum losses [Phys. Rev. D 104, 104020 (2021)], providing brick-type results whichwill be useful, e.g., in the high-accurate determination of the radiated impulses of the two bodiesundergoing a scattering process.

Gravitational radiation can be decomposed as an infinite sum of radiative multipole moments, which parametrize the waveform at infinity. The multipolar-post-Minkowskian formalism provides a connection between these multipoles and the source multipole moments, known as explicit integrals over the matter source. The gravitational wave energy, angular momentum, and linear momentum fluxes are then expressed as multipolar expansions containing certain combinations of the source moments. We compute several gauge-invariant quantities as "building blocks"entering the multipolar expansion of both radiated energy and angular momentum at the 2.5 post-Newtonian (PN) level of accuracy in the case of hyperboliclike motion, by completing previous studies through the calculation of tail effects up to the fractional 1PN order. We express such multipolar invariants in terms of certain eccentricity enhancement factor functions, which are the counterpart of the well-known enhancement functions already introduced in the literature for ellipticlike motion. Finally, we use the complete 2.5PN-accurate averaged energy and angular momentum fluxes to study the associated adiabatic evolution of orbital elements under gravitational radiation reaction.

We briefly review the known properties of Melvin's magnetic universe and study the propagation of test charged matter waves in this static spacetime. Moreover, the possible correspondence between the wave perturbations on the background Melvin universe and the motion of charged test particles is discussed. Next, we explore a simple scenario for turning Melvin's static universe into one that undergoes gravitational collapse. In the resulting dynamic gravitational field, the formation of cosmic double-jet configurations is emphasized.

We compute the metric fluctuations induced by a turbulent energy-matter tensor within the first orderpost-Minkowskian approximation. It is found that the turbulent energy cascade can in principle interferewith the process of black hole formation, leading to a potentially strong coupling between these two highlynonlinear phenomena. It is further found that a power-law turbulent energy spectrum EðkÞ ~ k-n generatesmetric fluctuations scaling as xn-2, where x is the four-dimensional spacelike distance from an arbitraryorigin in Minkowski spacetime, highlighting the onset of metric singularities whenever n < 2. Finally, theeffect of metric fluctuations on the geodesic motion of test particles is also discussed as a potentialtechnique to extract information on the spectral characteristics of fluctuating spacetime.

We compute the variation of the Fokker-Wheeler-Feynman total linear and angular momentum of agravitationally interacting binary system under the second post-Minkowskian retarded dynamics. Theresulting OðG2Þ equations-of-motion-based, total change in the system's angular momentum is found toagree with existing computations that assumed balance with angular momentum fluxes in the radiation zone.

A recently introduced approach to the classical gravitational dynamics of binary systems involves intricate integrals (linked to a combination of nonlocal-in-time interactions with iterated 1r-potential scattering) which have so far resisted attempts at their analytical evaluation. By using computing techniques developed for the evaluation of multiloop Feynman integrals (notably harmonic polylogarithms and Mellin transform) we show how to analytically compute all the integrals entering the nonlocal-in-time contribution to the classical scattering angle at the sixth post-Newtonian accuracy, and at the seventh order in Newton's constant, G (corresponding to six-loop graphs in the diagrammatic representation of the classical scattering angle).

The linear-order effects of radiation-reaction on the classical scattering of two point masses, in general relativity, are derived by a variation-of-constants method. Explicit expressions for the radiation-reaction contributions to the changes of 4-momentum during scattering are given to linear order in the radiative losses of energy, linear-momentum, and angular momentum. The polynomial dependence on the masses of the 4-momentum changes is shown to lead to nontrivial identities relating the various radiative losses. At order G3 our results lead to a streamlined classical derivation of results recently derived within a quantum approach. At order G4 we compute the needed radiative losses to next-to-next-to-leading-order in the post-Newtonian expansion, thereby reaching the absolute fourth and a half post-Newtonian level of accuracy in the 4-momentum changes. We also provide explicit expressions, at the absolute sixth post-Newtonian accuracy, for the radiation-graviton contribution to conservative O(G4) scattering. At orders G5 and G6 we derive explicit theoretical expressions for the last two hitherto undetermined parameters describing the fifth-post-Newtonian dynamics. Our results at the fifth-post-Newtonian level confirm results of [Nucl. Phys. B965, 115352 (2021)NUPBBO0550-321310.1016/j.nuclphysb.2021.115352] but exhibit some disagreements with results of [Phys. Rev. D 101, 064033 (2020)PRVDAQ2470-001010.1103/PhysRevD.101.064033].

The energy radiated (without the 1.5PN tail contribution which requires a different treatment) by a binary system of compact objects moving in a hyperboliclike orbit is computed in the frequency domain through the second post-Newtonian level as an expansion in the large-eccentricity parameter up to next-to-next-to-leading order, completing the time domain corresponding information (fully known in closed form at the second post-Newtonian of accuracy). The spectrum contains quadratic products of the modified Bessel functions of the first kind (Bessel K functions) with frequency-dependent order (and argument) already at Newtonian level, so preventing the direct evaluation of Fourier integrals. However, as the order of the Bessel functions tends to zero for large eccentricities, a large-eccentricity expansion of the spectrum allows for analytical computation beyond the lowest order.

The need for more and more accurate gravitational-wave templates requires taking into account all possible contributions to the emission of gravitational radiation from a binary system. Therefore, working within a multipolar-post-Minkowskian framework to describe the gravitational-wave field in terms of the source multipole moments, the dominant instantaneous effects should be supplemented by hereditary contributions arising from nonlinear interactions between the multipoles. The latter effects include tails and memories and are described in terms of integrals depending on the past history of the source. We compute higher-order tail (i.e., tail-of-tail, tail-squared, and memory) contributions to both energy and angular momentum fluxes and their averaged values along hyperboliclike orbits at the leading post-Newtonian approximation, using harmonic coordinates and working in the Fourier domain. Because of the increasing level of accuracy recently achieved in the determination of the scattering angle in a two-body system by several complementary approaches, the knowledge of these terms will provide useful information to compare results from different formalisms.

This paper proposes a toy model where, in the Einstein equations, the right-hand side is modified by the addition of a term proportional to the symmetrized partial contraction of the Ricci tensor with the energy-momentum tensor, while the left-hand side remains equal to the Einstein tensor. Bearing in mind the existence of a natural length scale given by the Planck length, dimensional analysis shows that such a term yields a correction linear in ? to the classical term that is instead just proportional to the energy-momentum tensor. One then obtains an effective energy-momentum tensor that consists of three contributions: pure energy part, mechanical stress, and thermal part. The pure energy part has the appropriate property for dealing with the dark sector of modern relativistic cosmology. Such a theory coincides with general relativity in vacuum, and the resulting field equations are here solved for a Dunn and Tupper metric, for departures from an interior Schwarzschild solution as well as for a Friedmann-Lemaitre-Robertson-Walker universe.

In Cosmology and in Fundamental Physics there is a crucial question like: where the elusive substance that we call Dark Matter is hidden in the Universe and what is it made of? that, even after 40 years from the Vera Rubin seminal discovery [1] does not have a proper answer. Actually, the more we have investigated, the more this issue has become strongly entangled with aspects that go beyond the established Quantum Physics, the Standard Model of Elementary particles and the General Relativity and related to processes like the Inflation, the accelerated expansion of the Universe and High Energy Phenomena around compact objects. Even Quantum Gravity and very exotic Dark Matter particle candidates may play a role in framing the Dark Matter mystery that seems to be accomplice of new unknown Physics. Observations and experiments have clearly indicated that the above phenomenon cannot be considered as already theoretically framed, as hoped for decades. The Special Topic to which this review belongs wants to penetrate this newly realized mystery from different angles, including that of a contamination of different fields of Physics apparently unrelated. We show with the works of this ST that this contamination is able to guide us into the required new Physics. This review wants to provide a good number of these "paths or contamination" beyond/among the three worlds above; in most of the cases, the results presented here open a direct link with the multi-scale dark matter phenomenon, enlightening some of its important aspects. Also in the remaining cases, possible interesting contacts emerges. Finally, a very complete and accurate bibliography is provided to help the reader in navigating all these issues.

The post-Minkowskian approach to gravitationally interacting binary systems (i.e., perturbation theory in G, without assuming small velocities) is extended to the computation of the dynamical effects induced by the tidal deformations of two extended bodies, such as neutron stars. Our derivation applies general properties of perturbed actions to the effective field theory description of tidally interacting bodies. We compute several tidal invariants (notably the integrated quadrupolar and octupolar actions) at the fast post-Minkowskian order. The corresponding contributions to the scattering angle are derived.